THE INFLUENCE OF NUMERICAL ERRORS ON DETERMINING THE DISTRIBUTION OF VALUES OF STOCHASTIC IMPULSES FORCING AN OSCILLATOR

Authors

  • Marian Jabłoński Jagiellonian University
  • Agnieszka Ozga AGH University of Science and Technology

Keywords:

stochastic impulses, stochastic moments, distributions of impulses, Poisson process

Abstract

The motion of an oscillator excited by a Poisson process is a stochastic process Xt. Knowing the trajectory of the motion we can find all the stochastic moments of Xt. for large t. This, in turn, allows us to find stochastic distribution of the forces exciting an oscillator. In this paper we evaluate the impact of errors in the computations of the moments on computed distribution of the forces exciting an oscillator.

Downloads

Download data is not yet available.

References

Billingsley P. 1987, Prawdopodobieństwo i miara. PWN, Warszawa.

Campbell N. 1909a, The study of discontinuous phencmena. Proceedings of the Cambridge Philosophical Society, 15.

Campbell N. 1909b, Discontinuities in light emission. Proc. Cambr. Phil. Soc., 15.

Hurwitz H., Kac M. 1944, Statistical analysis of certain types of random functions. Annals of Math. Stat., 15.

Iwankiewicz R., Nielsen S.R.K. 1996, Dynamic response of non-linear systems to renewal impulses by path integration. J. Sound Vib. Mech., vol. 195, Issue 2.

Iwankiewicz R. 2003, Dynamic systems under random impulses driven by a generalized Erlang renewal process. In: Proceedings of the 10th IFIP, WIG 7.5 Working Conference on Reliability and Optimization of Structural Systems, 25-27 March 2002, Kansai University, Osaka, Japan.

Iwankiewicz R. 2002, Dynamic response of non-linear systems to random trains of non-overlapping pulses. Meccanica, 37.

Jabłoński M., Ozga A. 2006a, On statistical parameters characterizing vibrations of oscillators without damping and forced by stochastic impulses. Mechanics, vol. 25, No. 4.

Jabłoński M., Ozga A. 2006b, Parameters characterising vibrations of oscilators with damping forced by stochastic impulses. Archives of Acoustics, 31.

Jabłoński M., Ozga A. 2006c, Parametry charakteryzujące wymuszone stochastycznie drgania układu o jednym stopniu swobody z tłumieniem nadkrytycznym, podkrytycznym i krytycznym. Wibrotech.

Jabłoński M., Ozga A. 2010, Distribution of stochastic impulses acting on an oscillator as a function of its motion. Acta Physica Polonica A, vol. 118, No. 1.

Khintchine A. 1938, Theorie des abklingenden Spontaneffektes. Bull. Acad. Sci URSS, Ser. Math., 3.

Rice S. 1944: Mathematical analysis of random noise I. Bell. System Technical Journal, 23.

Roberts J.B. 1965a, On the Harmonic Analysis of Evolutionary Random Vibrations. J. Sound Vibr., 1965.

Roberts J.B. 1965b, The Response of Linear Vibratory Systems to Random Impulses. J. Sound Vibr., 2.

Roberts J.B. 1972, System Response to Random Impulses. J. Sound Vibr., 24.

Roberts J.B. 1973, Distribution of the Response of Linear Systems toPios-son Distributed Random Pulses. J. Sound Vibr., 28.

Roberts J.B., Spanos P.D. 1986, Stochastic Averaging: an Approximate Method for Solving Random Vibration Problems. Int. J. Non-Linear Mech., 21 (2).

Rowland E.N. 1936, The theory of mean square variation of a function formed by adding; known functions with random phases and applications to the theories of shot effect and of light. Proc. Cambr. Phil. Soc., 32.

Takac L. 1954, On secondary processes generated by a Poisson process and their applications in physics. Acta Math. Acad. Sci. Hungar. 5.

Tylikowski A. 1991, Stochastyczna stateczność układów ciągłych. PWN, Warszawa.

Downloads

Published

2011-01-17

Issue

Vol. 29 No. 4 (2010)

Section

Articles

License

Remember to download, sign, scan and attach the copyright notice

This file should be uploaded as a Supplementary file (Step 4) of the submission procedure.